An economic theory that calls for workers to take control of factories is

This is an *element* of socialism, aka market socialism. You can read more details by searching 'worker's self-management' on Wikipedia. I'd link it, but links aren't allowed here.

The idea is that all workers participate in the decision making/administration and therefore all workers get portions of the profits the company makes.

Be aware that this is only a piece though, there's a lot more that make it up.

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